Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
0.5 kgk = 140 N/m

A 0.5 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.5 kgk = 140 N/m
f = Hz
2.Easy
3.5 kgk = 390 N/m

A 3.5 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the period T.

m = 3.5 kgk = 390 N/m
T = s
3.Medium
L = 1.6 mT = 2.67 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 2.67 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 2.67 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
5.Hard
2.9 kgk = 320 N/mA = 2 cm

A 2.9 kg mass on a spring with k = 320 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.9 kgk = 320 N/mA = 2 cm
E = J
6.Hard
1 kgk = 1400 N/m250 m/s

A 20 g bullet moving at 250 m/s hits and stays in a 1 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 250 m/sM = 1 kgk = 1400 N/m
A = cm

Answer key

  1. 1. f = 2.663 Hz
  2. 2. T = 0.5952 s
  3. 3. g = 8.86 m/s²
  4. 4. L = 0.487 m
  5. 5. E = 0.064 J
  6. 6. A = 13.23 cm

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